Ilse Fischer

u:find@Universität Wien  
Combinatorics Group@Universität Wien

Papers:

1. (with Seamus P. Albion, Theresia Eisenkölbl, Moritz Gangl, Hans Höngesberg, Christian Krattenthaler and Martin Rubey) ”A generalization of conjugation of integer partitions”
   arXiv:2407.16043
   
2. (with Roger Behrend and Christoph Koutschan) ”Diagonally symmetric alternating sign matrices”
   arXiv:2309.08446
   
3. (with Seamus P. Albion, Hans Höngesberg and Florian Schreier-Aigner) ”Skew symplectic and orthogonal characters through lattice paths”,
   European J. Combin. 122 (2024).
   arXiv:2305.11730
   
4.  “Bounded Littlewood identity related to alternating sign matrices’’,
   Forum Math. Sigma  12 (2024).
   arXiv:2301.00175
   
5. (with Florian Schreier-Aigner) “(-1)-Enumerations of arrowed Gelfand-Tsetlin patterns’’,
   European J. Combin. 120 (2024).
   arXiv:2302.04164
   companion.nb and data.mx
   
6. (with Hans Höngesberg) “Alternating sign matrices with reflective symmetry and plane partitions: n+3 pairs of equivalent statistics”,   
   arXiv:2207.04469
   
7. (with Florian Schreier-Aigner) “Alternating sign matrices and totally symmetric plane partitions,   
   Algeb. Combin. 7 (2024).
   arXiv:2201.13142
   
8. (with Hans Höngesberg and  Florian Schreier-Aigner) ”Alternating sign matrices and descending plane partitions: a linear number of equivalent statistics”,
   Sem. Lothar. Combin. 89B, Proceedings of FPSAC’23.
   
9.  (with Florian Schreier-Aigner) “The relation between alternating sign matrices and descending plane partitions: n+3 pairs of equivalent statistics”,   
   Adv. Math. 413 (2023).
   arXiv:2106.11568
   
10.  “Computations versus bijections in tiling counting’’, 
    Adv. Appl. Math. 142 (2023), 49pp.
    
11.  (with Matjaž Konvalinka) “The mysterious story of square ice, piles of cubes, and bijections”, 
    PNAS 2020, PDF 
    
12.  (with Florian Schreier-Aigner, Matjaž Konvalinka, Philippe Nadeau, and Vasu Tewari) “Alternating Sign Matrices and Totally Symmetric Plane Partitions”, 
    Sem. Lothar. Combin. 84B, Proceedings of FPSAC’20. 
    arXiv:2005.12448 
    
13.  (with Matjaž Konvalinka) “The first bijective proof of the refined ASM theorem”, 
    Sem. Lothar. Combin. 84B, Proceedings of FPSAC’20. PDF 
    
14. (with Matjaž Konvalinka) “A bijective proof of the ASM theorem, Part II: ASM enumeration and ASM-DPP relation”, 
    Int. Math. Res. Not. IMRN 2022, no. 10, 7203-7230.
    arXiv:1912.01354 
    
15. (with Mihai Ciucu) “Lozenge tilings of hexagons with removed core and satellites”, 
    Annales de l’Institut Henri Poincaré D 10 (2023).
    arXiv:1910.11004,
    
16. (with Matjaž Konvalinka ) “A bijective proof of the ASM theorem, Part I: the operator formula”, 
    Elect. J. Combin. 27, P3.35, 29 pages. 
    arXiv:1910.04198 
    
17. (with Manjil P. Saikia ) “Refined Enumeration of Symmetry Classes of Alternating Sign Matrices”, 
    J. Combin. Theory Ser. A 178 (2021). 
    arXiv:1906.07723
    
18. (with Arvind Ayyer ) “Bijective proofs of skew Schur polynomial factorizations”, 
    J. Combin. Theory Ser. A 174 (2020). 
    arXiv:1905.05226 
    
19. A constant tern approach to enumerating alternating sign trapezoids”, 
    Adv. Math. 356 (2019). 
    arXiv:1804.08681 
    
20. “Enumeration of alternating sign triangles using a constant term approach”, 
    Trans. Amer. Math. Soc. 372 (2019), 1485–1508. 
    arXiv:1804.03630 
    
21. “Constant term formulas for refined enumerations of Gog and Magog trapezoids”, 
    J. Combin. Theory Ser. A 158 (2018), 560–604. 
    arXiv:1804.07054 
    
22. (with Arvind Ayyer and Roger Behrend ) “Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order”, 
    Adv. Math. 367 (2020). 
    arXiv:1611.03823 
    
23. “Short proof of the ASM theorem avoiding the six-vertex model”, 
    J. Combin. Theory Ser. A 144 (2016), 139-156. Fifty Years of the Journal of Combinatorial Theory! PDF
    
24. “Counting integer points in polytopes associated with directed graphs”, 
    Adv. Appl. Math. 79 (2016), 125-153. PDF 
    
25. (with Roger Behrend and Matjaž Konvalinka ) “Diagonally and antidiagonally symmetric alternating sign matrices of odd order”, 
    Adv. Math. 315 (2017), 324–365. 
    arXiv:1512.06030 
    
26. (with Mihai Ciucu) “Lozenge tilings of hexagons with arbitrary dents “, 
    Adv. Appl. Math. 73 (2016), 1-22. 
    arXiv:1412.3945 
27. (with Sabine Beil and Philippe Nadeau ) “Wieland gyration for triangular fully packed loop configurations “, 
    Elect. J. Combin. 22, P1.26, 17 pages. 
    arXiv:1406.1657 
28. (with Lukas Riegler ) “Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity”, 
    Elect. J. Combin. 22, P1.5, 32 pages. 
    arXiv:1403.0535
    An Oberwolfachreport on this topic.
29. (with Mihai Ciucu ) “Proof of two conjectures of Ciucu and Krattenthaler on the enumeration of lozenge tilings of hexagons with cut off corners”, 
    J. Combin. Theory Ser. A 133 (2015), 228-250. 
    arXiv:1309.4640 
30. (with Martina Juhnke-Kubitzke ) “Spectra and eigenvectors of the Segre transformation”, 
    Adv. Appl. Math. 56 (2014), 1-19. 
    arXiv:1303:5358 
31. (with Philippe Nadeau ) “Fully Packed Loops in a triangle: matchings, paths and puzzles”, 
    J. Combin. Theory Ser. A 130 (2015), 64-118. 
    arXiv:1209.1262 
32. (with Mihai Ciucu ) 
    “A triangular gap of size two in a sea of dimers on a 60 degree angle”, J. Phys. A: Math. Theor. 45 (2012). 
    PDF 
33. (with Lukas Riegler ) “Combinatorial Reciprocity for Monotone Triangles”, 
    J. Combin. Theory Ser. A 120 (2013), 1372 – 1393. 
    arXiv:1111.2695
    accepted for a FPSAC12 talk 
34. “Sequences of labeled trees related to Gelfand-Tsetlin patterns “, 
    Adv. Appl. Math. 49 (2012), 165 — 195. 
    arXiv:1104.0568v1 
35. “Linear relations of refined enumerations of alternating sign matrices “, 
    J. Combin. Theory Ser. A 119 (2012), no. 2, 556 — 578. 
    arXiv:1008.0527v1 
36. “Refined enumerations of alternating sign matrices: monotone (d,m)-trapezoids with prescribed top and bottom row”, 
    J. Alg. Combin. 33 (2011), no. 2, 239 — 257. 
    arXiv:0907.0401 
37. (with Dan Romik) “More refined enumerations of alternating sign matrices”, 
    Adv. Math 222 (2009), Issue 6, 2004 — 2035. 
    arXiv:0903.5073
    Mathematica-Package
38. “The operator formula for monotone triangles — simplified proof and three generalizations”, 
    J. Combin. Theory Ser. A. 117 (2010), 1143 — 1157. 
    arXiv:0903.4628 
39. “An operator formula for the number of halved monotone triangles with prescribed bottom row”, 
    J. Combin. Theory Ser. A 116 (2009), no. 3, 515 — 538. 
    math.CO/0702637
40. “A new proof of the refined alternating sign matrix theorem”, 
    J. Combin. Theory Ser. A 114 (2007), no. 2, 253 — 264. 
    math.CO/0507270 
41. “The number of monotone triangles with prescribed bottom row”, 
    Adv. Appl. Math. 37 (2006), no. 2, 249 — 267. 
    math.CO/0501102 
42. (with Gerald Gruber, Franz Rendl and Renata Sotirov) “Computational experience with a bundle approach for semidefinite cutting plane relaxations of Max-Cut and Equipartition”, 
    Math. Program., Ser. B 105 (2006), 451 — 469. 
43. “Another refinement of the Bender-Knuth (ex-)Conjecture”, 
    European J. Combin. 27 (2006), 290 — 321. 
    math.CO/0401235
    Mathematica-file with some hypergeometric identities used in the paper
44. “A method for proving polynomial enumeration formulas”, 
    J. Combin. Theory Ser. A 111 (2005), 37 — 58. 
    math.CO/0301103
45. (with Charles H. C. Little) “Even circuits of prescribed clockwise parity”, 
    Elect. J. Combin. 10, R45, 20 pages. 
    math.CO/0203281
46. “A symmetry theorem on a modified jeu de taquin”, 
    European J. Combin. 23 (2002), 929 — 936. 
    math.CO/0112263
47. “A bijective proof of the hook length formula for shifted standard tableaux”, preprint, December 2001. 
    math.CO/0112261
48. “Moments of inertia associated with the lozenge tilings of a hexagon”, 
    Sem. Lothar. Combin. 45 (2000/01), Art B45f, 14pp. (electronic). 
    math.CO/0012126
49. (with Charles H.C. Little) “A characterisation of Pfaffian near bipartite graphs”, 
    J. Combin. Theory Ser. B 82 (2001), no. 2, 175 — 222. 
    math.CO/0002062
50. (with Charles H. C. Little and Franz Rendl) “Towards a characterisation of Pfaffian near bipartite graphs”, 
    Discrete Math. 244 (2002), 279 — 297. 
    math.CO/9909026
51. “Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus in the centre”, 
    J. Combin. Theory Ser. A 96 (2001), no. 1, 31 — 88. 
    math.CO/9906102 

Some talks:

• Alternating Sign Arrays and Littlewood-type identities, ICECA 2024, Video from ICECA 2024
• Alternating Sign Arrays and Plane Partitions, SLC 90
•  New Littlewood-type identities and the sequence 1, 4,60, 3328,…      
• Bounded Littlewood-type identities and alternating sign matrices 
• Alternating sign matrices and descending plane partitions: n+3 pairs of equivalent statistics , Video from “Lattice Paths, Combinatorics and Interactions, 2021, CIRM 
• Where are the bijections ? Plane partitions and alternating sign matrices
• Bijective proofs of (skew) Schur polynomial factorizations, Video from the 2020 cms winter meeting.
• First bijective proofs of ASM theorems: short and long. Video from FPSAC 2020 and Video from AofA 2020.
• Alternating sign trapezoids and cyclically symmetric lozenge tilings with a central hole
• Extreme DASASMs of odd order
• FPSAC talk on DASASMs
• Proof of the DASASM-conjecture
• Lozenge tilings of hexagons with arbitrary dents, other version
• Extreme DADASMs
• Vertically symmetric alternating sign matrices and a multivariate laurent polynomial identity
• Fully packed loop configurations on a triangle for experts and for newcomers
• An alternative approach to alternating sign matrices
• Sequences of labeled trees related to gelfand-tsetlin patterns
• Refined enumerations of alternating sign matrices
• Die Mathematik des Käse-Kästchen-Spiels (Schüler*innentag)
• A new proof of the refined alternating sign matrix theorem
• The number of monotone triangles with prescribed bottom row
• Die Geschichte der alternierenden Vorzeichenmatrix Vermutung
• Polynomiale Abzählformeln
• A method for proving polynomial enumeration formulas
• A bijective proof of the hook-length formula for shifted standard tableaux
• A youtube talk of my father on education!

• Doctoral Students
• Teaching
• CV
• David P. Robbins Prize 2019 of the AMS: Prize Booklet and Video

Theses:

• “Der Satz von Skolem, Mahler, Lech – ein Ergebnis über die Nullstellen linearer Rekursionsfolgen”, Master thesis, Vienna 1997. 
• “Enumeration of perfect matchings: Rhombus tilings and Pfaffian graphs”, Doctoral thesis, Vienna 2000. 
• “A polynomial method for the enumeration of plane partitions and alternating sign matrices”, Habilitation thesis, Vienna 2005. 

My very first paper:

• “A simple new proof of the Primitive Element Theorem”, Vienna 1996.